The uncertainty in the position of an electro | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Given velocity $v = 300 \, ms^{-1}$ and accuracy $=

Vedclass · Accepted Answer

$1.92 	imes 10^{-2} \, m$

Vedclass · Answer

(B) According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Given velocity $v = 300 \, ms^{-1}$ and accuracy $= 0.001 \%$.Uncertainty in velocity $\Delta v = \frac{0.001}{100} 	imes 300 = 3 	imes 10^{-3} \, ms^{-1}$.Using $\Delta x = \frac{h}{4\pi m \Delta v}$:$\Delta x = \frac{6.63 	imes 10^{-34}}{4 	imes 3.14 	imes 9.1 	imes 10^{-31} 	imes 3 	imes 10^{-3}}$.$\Delta x = \frac{6.63 	imes 10^{-34}}{342.31 	imes 10^{-34}} \approx 0.01937 \, m \approx 1.92 	imes 10^{-2} \, m$.

The uncertainty in the position of an electron (mass = $9.1 \times 10^{-31} \, kg$) moving with a velocity of $300 \, ms^{-1}$ with an accuracy of $0.001 \%$ is ...... $(h = 6.63 \times 10^{-34} \, Js)$

Similar Questions

Provide the equation for a system where the energy of an atom or molecule does not change with time.

Which one of the following conditions is incorrect for a well-behaved wave function $(\psi)$?

Which of the following statements does not form part of Bohr's model of the hydrogen atom?

Find the uncertainty in the position of an electron which is moving with a velocity of $2.99 \times 10^4 \ cm \ s^{-1}$,accurate up to $0.0016 \%$. (Given,$m_e = 9.1 \times 10^{-28} \ g, h = 6.626 \times 10^{-27} \ erg \cdot s$)

$A$ microscope using suitable photons is employed to locate an electron in an atom within a distance of $0.1 \, \mathring{A}$. What is the uncertainty involved in the measurement of its velocity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module